FIG. 1: Evolutionary dynamics of two competing populations with HGT in a fixed and in a fast-oscillating environment.

Left, fixed/averaged environment; right, oscillating environment. The coarse-grained time variations of the fractions of each population and the total abundance of both populations are described by the replicator dynamics with density dependent payoff matrices. The fitness of each population is comprised of two terms obtained from two different evolutionary games. These evolutionary games represent the interaction between the two populations in the fixed/averaged and varying environments (left and right matrices, respectively). In the left matrix, $r_A$ and $r_B$ are reproduction rates of the populations $A$ and $B$ in the averaged/fixed environment, respectively. The competitions within and between the two populations are given by $a_{ij}$, $i,j=1,2$ rates. $\gamma$ is the gene transfer balance in the averaged/fixed environment. $\xi$ and $\kappa$ represent environmental variations in the model, these are defined by the product of oscillatory parts of reproduction and gene transfer balance rates, defined in (11). $N$ is the total abundance of both populations.